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if y = sec ( tan^(-1) x) then (dy)/(dx)...

if `y = sec ( tan^(-1) x) ` then` (dy)/(dx)` is

A

`1//2`

B

1

C

`sqrt(2)`

D

`1sqrt(2)`

Text Solution

Verified by Experts

`y=sec(tan^(-1)x)`
`rArr" "(dy)/(dx)=sec (tan^(-1)x)cdottan (tan^(-1)x)cdot(1)/(1+x^(2))`
`rArr" "((dy)/(dx))_(x=1)=sec((pi)/(4))tan((pi)/(4))(1)/(1+1)=(1)/(sqrt(2))`
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Knowledge Check

  • If y = sec ( tan^(-1) x) , then ( dy)/( dx) at x = 1 is equal to

    A
    `1//2`
    B
    1
    C
    `sqrt(2)`
    D
    `1//sqrt(2)`

  • If y = sec ( tan^(-1) x) then (dy)/( dx) at x = 1 is equal to

    A
    ` (1)/( sqrt(2))`
    B
    ` - (1)/( sqrt(2)) `
    C
    1
    D
    None of these

  • If y= sec tan^(-1) "" ,then (dy)/(dx) =

    A
    `x//(1+x^2)`
    B
    `x sqrt""(1+ x^2)`
    C
    `1// sqrt((1+x^2)`
    D
    `x//sqrt(1+x^2)`

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